True or false on the first law and expansion

Problem

True or false, justifying each answer:

1. The first law holds for both reversible and irreversible processes.
2. In a free expansion into a vacuum the gas always cools down.
3. At constant volume, all the heat supplied to the gas turns into internal energy.
4. The work done by the atmosphere on an expanding gas is positive.

Solution

1) TRUE. The first law is conservation of energy: it does not require reversibility. It holds for any process, including irreversible ones in which the intermediate states are not equilibrium states.

2) FALSE. In free expansion the container is isolated ($Q = 0$) and the gas expands into a vacuum ($L = 0$), so $\Delta E_\text{int} = 0 \Rightarrow T$ constant. The gas does not cool down.

3) TRUE. At constant volume $L = 0$, so the first law gives $Q = \Delta E_\text{int}$: all the heat becomes internal energy.

4) FALSE. If the gas expands, it compresses the atmosphere: $\Delta V_\text{atm} < 0$, so $L_\text{atm} = P_\text{atm}\,\Delta V_\text{atm} < 0$. In the gas’s balance, the atmosphere appears with negative work.

$\ev{T,\ F,\ T,\ F}$

Links

Topics: Thermodynamics Concepts: First law of thermodynamics · Thermodynamic processes